Find a Quadratic Polynomial Whose Zeroes are -4 and 2

A quadratic polynomial is of the form f(x) = ax²+bx+c and a ≠ 0

Answer: x² + 2x - 8 is the Quadratic Polynomial Whose zeroes are -4 and 2

Let us see, how to solve.

Explanation:

A quadratic polynomial in terms of the zeroes (α,β) is given by

x² - (sum of the zeroes) x + (product of the zeroes)

i.e,

f(x) = x² - (α +β) x +αβ

Now,

Given that zeroes of a quadratic polynomial are -4 and 2

let α = -4 and β= 2

Therefore, substituting the value α = -4 and β= 2  we get

f(x) = x² - (α + β) x + αβ

= x² - ( -4 + 2) x +(-4)(2)

= x² + 2x - 8

Thus, x² + 2x - 8 is the quadratic polynomial whose zeroes are -4 and 2.